Development of fuzzy X¯∼-R∼ and X¯∼-S∼ control charts using α-cuts

Statistical process control (SPC) is an approach that uses statistical techniques to monitor the process. Shewhart introduced the control charts that are one of the most important techniques of quality control to detect if assignable causes exist. The widely used control charts are X¯-R and X¯-S. These are called traditional variable control charts. In the traditional variable control charts, center line, upper control limit and lower control limit are represented by numeric values. A process is either “in control” or “out of control” depending on numeric observation values. For many problems, control limits could not be so precise. Uncertainty comes from the measurement system including operators and gauges, and environmental conditions. In this context, fuzzy set theory is a useful tool to handle this uncertainty. Numeric control limits can be transformed to fuzzy control limits by using membership functions. If a sample mean is too close to the control limits and the used measurement system is not so sensitive, the decision may be faulty. Fuzzy control limits provide a more accurate and flexible evaluation. This study constructs the fuzzy X¯∼-R∼ and X¯∼-S∼ control charts with α  -cuts. An application is presented for fuzzy X¯∼-R∼ control charts. By using fuzzy X¯∼-R∼ and X¯∼-S∼ control charts, the flexibility of traditional control limits is increased.